"""Compares two numerical answers after normalizing their formats.

This function normalizes the input answers by removing commas and dollar signs, and
converting percentages to their decimal equivalents. It then compares the numerical
values to determine if they are approximately equal within a small tolerance.

Args:
    ans_p (str or None): The first answer to compare. Can be a string representing a
        number, optionally including commas, dollar signs, or a percentage. If None,
        the function immediately returns False.
    ans_l (str): The second answer to compare. Can be a string representing a number,
        optionally including commas, dollar signs, or a percentage.

Returns:
    bool: True if the normalized numerical values of `ans_p` and `ans_l` are within
        1e-3 of each other, False otherwise. Returns False if `ans_p` is None or if
        any conversion to float fails.

Examples:
    >>> compare_numerical_ans('100', '100')
    True
    >>> compare_numerical_ans('100.001', '100.001')
    True
    >>> compare_numerical_ans('$100', '100')
    True
    >>> compare_numerical_ans('100%', '1')
    True
    >>> compare_numerical_ans('1,000', '1000')
    True
    >>> compare_numerical_ans('0.000', '0.000')
    True
"""